How does one really compute inflation? I just now quickly looked up how the real GDP was computed. It is using the base year price to multiply the number of products traded. Is that meaningful? Is a ten year inflation computed on the base of the zeroth year price? The change in demand and supply would have made a huge change in the price when there is no inflation. The Motorola flip cell phone price now must be less than 1/100 of the price when it first came out. Does that mean there is severe deflation? On the other hand, the price for it could explode because it could have become a collector item. What about the price of a quantum computer --- the real one, or just something akin to DWave --- when it comes out? Are we going to compare its price against Von Neumann's Maniac or Allan Turing's Bombe or Intel 40386? This is nonsense and absurd. One rescue I can come up with right now, is we divide a finite time interval into multiple periods and computing recursively. We must assume the inflation speed is faster than the change of the supply and demand in each interval. I do not even know if that makes mathematical sense. Is there a proof of legitimacy for this or any other remedies, at least mathematically?

luchonacho has provided some sources below in his answer, particularly hedonic regression, for estimating the inflation. I have expressed my doubt over the efficacy of method. Here I would like to criticize the method further on the technicality.

The hedonic regression does not answer my question for distinguishing the change in supply and demand including that caused by the technological change. It seems the proponents of hedonic regression claim that it could make the distinction. Hedonic regression assumes the price of a good as the linear function of its attributes. Suppose the attributes have not changed over the period under consideration. However, the supply and demand for this good have changed due to, say, technological innovation that either has made the good obsolete or more valued or made useful in completely different ways than before, as well as inflation. Unless one already know extraneous information either on the change in supply and demand or the inflation, there is no way one can distinguish inflation from the change in supply and demand.

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Your criticisms of GDP are valid, and have long been recognised in the literature and by statistical offices. For example, one of the issues your question deals with is quality changes. The case of hardware is particularly visible.

Several agencies do adjust for quality changes. A common method to do so is using hedonic regressions. The aim here is to obtain a "valuation" of all the different components of an item, like a PC. For example, using these regressions you can get an idea of the value consumers give to memory, graphic card, DVD reader, speed, etc. Then, new products can be adjusted using these values. An example of such regression for computers is here.

The ONS (which computes GDP for the UK) do attempt to adjust for quality. In fact, they consider "volume" of a product as a combination of both quantity and quality. They differentiate between two methods to evaluate volume. For some homogeneous goods like agricultural grains or energy products, where quality is less relevant, you simply compute the physical volume. Yet, for most of the products, heterogeneity makes such calculation impossible. The quality adjustment then comes from prices. The ONS uses the hedonic regression method for goods with "frequent model changes", but uses other methodologies too. For example, there is a major challenge in measuring change in quality of public services (like health care and education). For a detailed description on the ONS quality adjustment, check this article. Check here for public productivity measurement.

For other formal references, see this one. The latest UN System of National Accounts, in which most of countries are based to compute national statistics, also offer some guidance on quality adjustment (section 4, page 361, in particular).

$\begingroup$Thank you for the explanation. I took a quick look into hedonistic regression link. It is seriously doubtful, no delusional, to me that mere regression can capture the real price change affected by supply and demand. Basically, this amounts to predicting the price in the future. It is unimaginable this could be true especially in the area of technology and fashion, not even in novel publishing or movie making.$\endgroup$
– HansMay 30 '17 at 16:56

$\begingroup$If that is possible, every silicon valley investor would be a millionaire overnight; every stock trader would have made a killing especially because the stock market has the most abundant market data available, while there is a severe paucity of data in any other market. It seems to me this method is used mostly in real estate market. I think this is somewhat reasonable because the real estate market is afterall slow changing and the local factors affecting the real price from supply and demand is somewhat stable compared to other fast changing sectors. Even there, failures galore.$\endgroup$
– HansMay 30 '17 at 17:00

$\begingroup$The 2006 real estate market subprime loan collapse triggering the global recession is a prime case in point. The task for predicting the macroeconomic price change in the whole global economy is made even more impossible as you have take all the fast changing factors into account than mere predicting a single product price which is in the microeconomic realm,$\endgroup$
– HansMay 30 '17 at 17:12

$\begingroup$Most importantly, the test for the effectiveness of any predictive method is through out-of-sample tests. For price prediction, the ultimate measure is the profit-and-loss over a long period. Has any of the methods made consistent profit than some benchmark simple strategy, if they are applied to trade on the market?$\endgroup$
– HansMay 30 '17 at 19:30

$\begingroup$@Hans You are right in that these methods are imperfect. But notice they are not used to predict (future), but rather to estimate (past). No idea if they are used for arbitrage or investing strategies, but they surely could be used. If you are very keen on these topics, why not to study them further and come up with better ways to measure real output?$\endgroup$
– luchonachoMay 31 '17 at 8:50